Related papers: Accardi complementarity in $\mu$-deformed quantum …
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…
In standard quantum mechanics (QM), a state vector $| \psi \rangle$ may belong to infinitely many different orthogonal bases, as soon as the dimension $N$ of the Hilbert space is at least three. On the other hand, a complete physical…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates.…
We discuss here a weak and strong type estimate for fractional integral operators on Morrey spaces, where the underlying measure $\mu$ does not always satisfy the doubling condition.
Quantum measurements necessarily disturb the state of physical system. Once we perform a complete measurement, the system undergoes decoherence and loses its coherence. If there is no disturbance, the state retains all of its coherence. It…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
The present work is a brief review of the recent development in the relativistic quantum mechanics in the $(1/2)\oplus (0,1/2)$ representation space. It can be useful for graduate students in particle physics and quantum field theory.
The foundations of non-linear quantum mechanics are based on six postulates and five propositions. On a first quantised level, these approaches are built on non-linear differential operators, non-linear eigenvalue equations, and the notion…
In this work we will answer the following question: What remains of Quantum Mechanics when we transform the background space-time into a space modularized by observation or measurement regions ? This new moduli space is constructed by…
We show that an infinite set of q-deformed relevant operators close a partial q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The dynamics is described by the multicommutator: [H,..., [H, O]...], that follows a power…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption…
In relative locality theories the geometric properties of phase space depart from the standard ones given by the fact that spaces of momenta are linear fibers over a spacetime base manifold. In particular here it is assumed that the…